兰州理工大学学报

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (6): 156-159.

• 数理科学 • 上一篇    下一篇

广义C3模

王永铎*,秦丽芳   

  1. 兰州理工大学 理学院, 甘肃 兰州 730050
  • 收稿日期:2020-10-13 出版日期:2021-12-28 发布日期:2021-12-28
  • 通讯作者: 王永铎(1974-),男,甘肃靖远人,博士,教授.Email:ydwang@lut.edu.cn
  • 基金资助:
    国家自然科学基金(11861043)

Generalized C3 modules

WANG Yong-duo, QIN Li-fang   

  1. School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China
  • Received:2020-10-13 Online:2021-12-28 Published:2021-12-28

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摘要： 作为C3模的真推广,引入广义C3模(简称G-C3模)的概念,研究这类模的基本性质,证明遗传环R是右V-环当且仅当每个有限余生成R-模是G-C3模当且仅当每个有限余表示R-模是G-C3模.

关键词: C3模, G-C3模, V-环

Abstract: As a proper generalization of C3 modules, the concept of generalized C3 modules (briefly G-C3 modules) is introduced in this paper. Basic properties of these modules are studied and it is shown that a hereditary ring R is a right V-ring if and only if every finitely cogenerated R-module is a G-C3 module if and only if every finitely copresented R-module is a G-C3 module.

Key words: C3 module, G-C3 module, V-ring

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